Atmospheric gravity waves are buoyancy waves that can transport momentum and energy over large distances in the atmosphere. Primary sources are disturbances in the troposphere such as flow over topography, convective systems, or jets. Conservation of energy causes the amplitude of the gravity waves to grow nearly exponentially as they propagate upward into less dense air at higher altitudes. As the waves break and dissipate, they deposit their momentum and energy into the background atmosphere. This in turn affects the atmosphere over a wide range of scales, from the local generation of turbulence to the forcing of a large scale circulation (Fritts and Alexander, 2003; Alexander et al., 2010). This dynamical forcing is most prominent in the mesosphere and lower thermosphere (MLT), at altitudes of typically 50–130 km. Here a large fraction of upward-propagating gravity waves reach their maximum amplitudes and break. The resulting dynamical forcing causes a global-scale circulation in the mesosphere with strong upwelling in the summer polar region and downwelling in the winter polar region (Lindzen, 1981; Holton, 1982). Adiabatic cooling and heating connected to this circulation causes thermal conditions in the mesosphere to deviate far from radiative equilibrium. As one consequence, the polar summer mesosphere becomes the coldest place on Earth, with temperatures reaching well below 130 K despite permanently sunlit conditions. This makes the region the home of the highest clouds on Earth, noctilucent clouds (NLCs) (Thomas, 1991; Karlsson and Shepherd, 2018).

The role of gravity waves is further complicated as they interact with the background flow as they propagate through the middle atmosphere. This leads to an altitude-dependent filtering of the gravity wave spectrum by the wind field (e.g. Fritts and Alexander, 2003), including the wind components from the planetary waves and tidal waves. The gravity wave spectrum reaching higher altitudes thus carries an imprint of the dynamics at lower altitudes. This leads to a number of interesting teleconnections that can link conditions in widely separated regions of the atmosphere. Examples include the control of the summer mesosphere by lower atmospheric conditions in terms of inter- and intra-hemispheric coupling (Becker et al., 2004; Karlsson et al., 2007, 2011; Körnich and Becker, 2010; Gumbel and Karlsson, 2011; Karlsson and Becker, 2016). Interactions between gravity waves and the mean flow can also give rise to a generation of secondary waves in the mesosphere. Gravity waves can generate planetary waves, either directly through zonally non-uniform dissipation (Holton, 1984), or indirectly through induced baroclinic instability in the vicinity of jets (Plumb, 1983; Sato and Nomoto, 2015). The breakdown of gravity waves generates secondary gravity waves that propagate both upward and downward. This happens through the creation of temporally and spatially localized momentum and energy fluxes, which in turn create strong local body forces and flow imbalances which then excite the secondary waves (Vadas et al., 2003; Fritts et al., 2006; Becker and Vadas, 2018).

While today the basic nature of the wave-driven circulation of the middle atmosphere is understood, important mechanisms and interactions remain to be quantified. Most notably, this concerns wave sources, wave dissipation, and the resulting forcing of the mean flow. A decisive quantity to be specified is the directional momentum flux, including its altitude dependence and its spectral distribution with regard to horizontal and vertical wavelengths. Today, many general circulation models can explicitly simulate gravity waves with longer horizontal and vertical wavelengths, while shorter sub-grid waves need to be parameterized, e.g. in terms of the “wave drag” that they exert on the mean flow (Alexander et al., 2010; Geller et al., 2013). Rather than accounting for the detailed underlying physics, these wave parameterizations are often used as a means of tuning the model to ensure realistic output, e.g. in terms of middle atmospheric wind fields or temperature fields. Recently, important steps have been taken towards creating self-consistent gravity-wave-resolving general circulation models (H.-L. Liu et al., 2014; Watanabe et al., 2015; Becker and Vadas, 2018). Complementary to these developments, ray-tracing models are important tools for case studies of wave events and comparisons to specific observational datasets (e.g. Marks and Eckerman, 1995; Preusse et al., 2006; Kalisch et al., 2014). A goal of ongoing model developments is to explicitly describe the entire chain from the lower atmospheric source region, via the lower and middle atmospheric wave filtering, to the wave effects in the MLT. Only wave-resolved simulations can be expected to describe the physics of, for example, intermittent wave interactions, energy cascades, and turbulence generation (Becker, 2012).

Observational data are critical for supporting such model developments, in particular in the MLT, where gravity wave effects are most evident. Unfortunately, we are today lacking global observations of wave spectra arriving in the MLT, and even more so of the contribution of different parts of the wave spectra to momentum transfer. Such observations are not only desirable to constrain model results directly in the MLT. Rather, gravity wave observations in the MLT can serve as a benchmark for testing wave implementations throughout the lower and middle atmosphere: general circulation models need to correctly describe the chain of wave processes at all altitudes in order to correctly reproduce resulting gravity wave properties observed in the MLT. In addition to providing a relevant database of gravity wave spectra, MLT studies are also needed that allow for investigations of the three-dimensional structure of wave propagation. An important example is the refraction of gravity waves in the vicinity of the mesospheric jet (Sato et al., 2009; Preusse et al., 2009; Ern et al., 2011). Other three-dimensional propagation effects concern the interaction of gravity waves with the polar vortex (McLandress et al., 2012; de Wit et al., 2014; Wright et al., 2017) or the suggested refraction of gravity waves during sudden stratospheric warmings (Thurairajah et al., 2014; Ern et al., 2016).

A field of particular interest is the relationship between gravity waves and NLCs. As described above, the gravity-wave-driven large-scale circulation is the very cause of the extremely cold polar summer mesopause region, and thus a pre-condition for the formation of NLCs. On more local scales, gravity-wave-induced variations of temperature and vertical wind strongly affect NLC conditions, and can both cause, enhance, or prohibit the formation of the clouds (e.g. Rapp et al., 2002; Kaifler et al., 2018). At the same time, ground-based and space-based observations of NLCs are a primary source of our knowledge about gravity wave activity in the middle atmosphere (e.g. Witt, 1962; Chandran et al., 2009; Rong et al., 2018; Gumbel and Karlsson, 2011). Gravity waves may also play an important role in explaining other dynamical NLC features like so-called ice fronts or ice voids (Megner et al., 2018).

While the above descriptions have focused on gravity wave interactions with larger-scale waves and the mean flow from the lower atmosphere to the MLT, the importance of gravity waves extends well beyond these altitudes. The MLT can be regarded as a transition region where many fundamental changes occur in atmospheric properties. Examples are the transition from well-mixed, turbulent conditions to molecular diffusion, a transition to non-local thermodynamic equilibrium with a substantially increased lifetime of excited species, a transition to an extreme-UV radiative environment, or the transition to increasing importance of ionospheric processes. Various “layered phenomena” in the MLT can be regarded as manifestations of these transitions. Prominent phenomena include dayglow and nightglow; layers of metal, dust or ice; and various plasma processes – all demonstrating strong links to both below and above. Despite this fact, the altitude around 100 km has long been regarded as a dividing line between different research communities, separating the middle and upper atmosphere. This view has changed in recent decades and has today been replaced by a strong interest in “whole atmosphere” model approaches that emphasize the connecting rather than the dividing role of the MLT (e.g. Roble, 2000; Marsh et al., 2007; Akmaev, 2011). Wave processes play a central role in this respect, and in bridging the atmospheric communities.

In addition to comprehensive whole atmosphere modelling efforts, there has been growing observational evidence of thermospheric and ionospheric responses to wave processes in the lower and middle atmosphere. The dynamical morphology of thermosphere and ionosphere has been shown to be strongly connected to tidal waves (e.g. Anderson, 1981; Oberheide et al., 2009), but also to planetary waves (e.g. Chen, 1992; Forbes and Leveroni, 1992) and gravity waves (e.g. Röttger, 1977; Park et al., 2014; Forbes et al., 2016; Trinh et al., 2018; Vadas et al., 2019). A basic open question concerns the relative importance of primary, secondary, and higher-order gravity waves in propagating from the middle atmosphere to the thermosphere and ionosphere through a multi-step vertical coupling process (Becker and Vadas, 2018; Vadas and Becker, 2018, 2019). In the altitude range 100–300 km, gravity waves have been shown to create temperature variations of 50 K and density variations of 10 %–25 % over spatial scales of tens to hundreds of kilometres (Vadas and Liu, 2013). As the gravity waves interact with the background flow before reaching these altitudes, fingerprints of lower atmospheric sources and middle atmospheric circulation systems are transported well into the thermosphere and ionosphere (Siskind et al., 2012). A prominent example is dynamic coupling suggested to occur during sudden stratospheric warmings (Funke et al., 2010; Chau et al., 2011). Akmaev (2011) estimates that more than half of the regular daily and seasonal variability in the thermosphere and ionosphere is forced from below. Akmaev further concludes that the availability of global data on MLT dynamics and variability is a limiting factor for future scientific progress, thus contrasting the MLT to the “data-rich” lower atmosphere and upper thermosphere.

In summary, there is substantial need for global observations of gravity waves in the mesosphere and lower thermosphere. These datasets are needed to support and verify ongoing developments of general circulation models, concerning both gravity wave parameterizations and gravity-wave-resolved implementations. These datasets should provide (1) information about horizontal (and vertical) wave spectra in order to identify the dominant scales that govern interactions with the mean flow, larger-scale waves, and possibly secondary waves; (2) information about directional momentum flux as decisive quantity for these interactions; and (3) three-dimensional wave information in order to address detailed propagation and refraction effects in the vicinity relevant dynamical structures.

What is the current status regarding such global observations of gravity waves in the MLT? Several satellite missions have provided data on MLT structures that have been analysed in terms of wave activity on various scales. Most of these apply limb-viewing geometries in a number of spectral ranges. On the TIMED satellite, infrared limb measurements by the SABER instrument provide species and temperature distributions that allow for retrievals of gravity waves and planetary waves (Krebsbach and Preusse, 2007; Forbes et al., 2009; Preusse et al., 2009). The TIDI instrument provides MLT gravity wave data in terms of airglow Doppler wind measurements (Liu et al., 2009). On the ENVISAT satellite, infrared limb emission measurements by the MIPAS instrument cover the MLT and can provide large-scale wave structures that could also be traced into the thermosphere (Funke et al., 2010). From the SOFIE instrument on board the AIM satellite, gravity wave potential energy is inferred based on infrared solar occultation temperature retrievals throughout the stratosphere and mesosphere (X. Liu et al., 2014). Measurements by the SCIAMACHY instrument have been analysed in terms of MLT planetary wave structures in noctilucent clouds (von Savigny et al., 2007). On the Aura satellite, microwave limb measurements by the MLS instrument have provided mesospheric planetary wave data based on composition, temperature, and Doppler wind analysis (Limpasuvan et al., 2005; Wu et al., 2008). The above limb sounders can provide vertical retrieval resolutions down to a few kilometres. However, all gravity wave analysis from these limb measurements suffers from sparse horizontal sampling and the long line-of-sight integration, largely restricting the analysis to horizontal wavelengths exceeding several hundred kilometres.

Complementary to the above limb datasets, nadir-viewing satellite measurements have been analysed in terms of waves in the MLT, primarily focusing on horizontal wave structures. These studies employ observations of either noctilucent clouds or airglow layers. Basic wave parameters have been inferred from NLC observations by the UVIST instrument on board the MSX satellite (Carbary et al., 2000). On the AIM satellite, the CIPS instrument has provided comprehensive gravity wave information from near-nadir imaging of NLCs, resulting in wave climatologies covering horizontal wavelengths both above 100 km (Rusch et al., 2008; Chandran et al., 2009) and below 100 km (Rong et al., 2018). MLT gravity wave analysis based on nadir nightglow observations has been reported from the VIIRS instrument on board the NOAA/NASA Suomi satellite (Yue et al., 2014; Miller et al., 2015; Azeem et al., 2015), and the IMAP/VISI instrument on board the International Space Station (Perwitasari et al., 2016). All gravity wave analysis from these nadir imagers is largely restricted to information about horizontal wavelengths in the observed layer. For NLCs, however, information about vertical structures has recently been obtained by applying tomographic methods to the different viewing angles available from the AIM/CIPS observations (Hart et al., 2018).

For a more complete gravity wave analysis, three-dimensional retrievals are desirable that provide spatial structures extending both shorter than 100 km in horizontal wavelength and shorter than 10 km in vertical wavelength (Preusse et al., 2008). Being limited by either limb or nadir geometry, we are so far lacking such three-dimensional gravity wave data in the MLT. In the stratosphere, techniques have been developed to overcome these limitations. The AIRS instrument on board the AQUA satellite measures upwelling radiation in a large number of spectral channels, and gravity waves have been retrieved from the upper troposphere to the mid-stratosphere (Hoffmann and Alexander, 2009; Gong et al., 2012). Additional techniques have been developed to maximize horizontal wave information from AIRS, utilizing either across-track nadir scans (Wright et al., 2017) or data from multiple satellite tracks (Ern et al., 2017). Enhanced horizontal information can also be obtained by combining data from several sounding instruments, like multiple GPS radio occultations (Wang and Alexander, 2010; Schmidt et al., 2016), or combined data from the HIRDLS instrument on board the Aura satellite and radio occultations (Alexander, 2015).

The ultimate way to obtain three-dimensional information about gravity waves is to apply tomographic techniques. Tomographic retrievals have been applied to the limb-scanning instruments MIPAS on board ENVISAT (Carlotti et al., 2001; Steck et al., 2005) and MLS on board Aura (Livesey et al., 2006). In the mesosphere, tomographic retrieval has been applied to the limb-scanning Odin satellite to study NLCs by the OSIRIS optical spectrograph (Hultgren et al., 2013; Hultgren and Gumbel, 2014), and water vapour and temperature by the SMR microwave instrument (Christensen et al., 2015, 2016). For instruments specifically designed for tomography, limb imaging is preferable over the above limb-scanning techniques. In this way, the number of lines of sight through a given atmospheric volume can be maximized. This has been utilized by the infrared limb imager of the OSIRIS instrument on board Odin (Degenstein et al., 2003, 2004), and by the airborne GLORIA instrument (Ungermann et al., 2011; Kaufmann et al., 2015). Limb imaging also provides the possibility to go from two-dimensional to fully three-dimensional tomography. Ungermann et al. (2010) investigated requirements for gravity wave retrievals in the troposphere and stratosphere, emphasizing the need for a fully three-dimensional tomographic analysis. Krisch et al. (2018) discussed tomographic retrieval with special emphasis on the limited range of observation angles that are typically available from limb measurements.

In this paper, we describe a new satellite mission aiming at three-dimensional tomographic studies of gravity waves and other structures in the upper mesosphere and lower thermosphere. The MATS satellite will perform limb imaging of the O2 atmospheric band airglow in the near-infrared and of NLCs in the ultraviolet. In combination with the tomography, spectroscopic techniques will be applied to infer atmospheric temperature and composition from the O2 emissions, and microphysical cloud properties from the NLC measurements. A complementary camera will provide nadir imaging of structures in the O2 atmospheric band nightglow on smaller spatial scales. A similar mission with a focus on the O2 atmospheric band nightglow has recently been described by Song et al. (2017). As compared to the pure limb imaging by MATS, Song et al. (2017) envisage tomographic retrievals utilizing both limb and sub-limb viewing.

The next section describes the basic ideas of the MATS mission, with a focus on scientific objectives and resulting instrument requirements. Section 3 provides details about the instrument design. Section 4 introduces the retrieval ideas behind MATS and the basic data processing. Section 5 describes operational planning. Section 6 concludes with a summary and some perspectives towards scientific collaboration. Note that the idea of this paper is to provide a general overview over the mission. More comprehensive details about instruments, retrieval methods, and scientific analysis will be published in separate papers.

The primary goal of MATS is to determine the global distribution of gravity waves and other structures in the MLT over a wide range of spatial scales. Primary measurement targets are airglow in the O2 atmospheric band and sunlight scattered from NLCs. These emissions will be measured in the altitude range 75–110 km and are to be analysed in terms of wave structures with horizontal wavelengths from tens of kilometres to global scales, and vertical wavelengths from 1 to 20 km. Over a period of 2 years, MATS will thus build up a geographical and seasonal climatology of wave activity in the MLT. This database will then be the starting point for scientific analysis in various directions. Relating back to the overview in Sect. 1, major scientific questions are as follows:  

What gravity wave spectra are present in the MLT, and how are these related to tropospheric sources and circulation conditions in the lower and middle atmosphere? These questions are tightly connected to wave–wave interactions such as filtering by planetary wave activity and in situ generation of secondary waves.

As described above, NLCs are one of the measurement targets of MATS. Since the pioneering days of NLC research, these clouds have transformed from a basic research object to a valuable research tool when it comes to remote sensing of the state of the MLT. Nonetheless, beyond using NLCs as a convenient tracer for gravity wave studies, the MATS science objectives also include NLCs in their own right:  

How are NLCs affected by gravity waves and other transient processes in the MLT? This concerns both the microphysics of ice particles and the resulting evolution of observable cloud structures.

The above scientific objectives define the requirements on the measurements that MATS will perform. Tomography is the basis for obtaining three-dimensional information on spatial scales that are relevant for gravity wave studies. The tomographic retrieval needs input in terms of multiple line-of-sight observations through a given atmospheric volume. This is achieved by a limb imager that observes the atmosphere along the Earth's tangent direction, with a field of view covering tangent altitudes between 75 and 110, and 300 km across the track. Figure 1 illustrates the observation geometry. In order to tomographically retrieve gravity wave information in the MLT, we need to utilize atmospheric emissions that are both sufficiently bright and susceptible to gravity wave activity. In the case of MATS, we utilize airglow in the O2 atmospheric band and scattering of sunlight by NLCs. Both O2 atmospheric band airglow and NLCs feature horizontal and vertical structures that are a direct response to gravity wave activity. As an additional benefit, both phenomena allow for a deeper analysis by applying spectroscopic techniques.

On MATS, the O2 atmospheric band is measured using four spectral channels in the near infrared between 750 and 775 nm (see Table 4 for details). Measurements will be performed both during daytime (dayglow) and nighttime (nightglow). As a primary step, the tomographic analysis will convert measured limb radiances to volume emission rates. Combining the four channels, subsequent spectroscopic analysis will utilize the rotational structure of the O2 atmospheric band emission to infer temperature (Babcock and Herzberg, 1948; Sheese et al., 2010). At the same time, the total volume emission rate in the O2 atmospheric band can be analysed in terms of odd oxygen densities: the atmospheric band nightglow provides a direct measure of atomic oxygen density (McDade et al., 1986; Murtagh et al., 1990). The atmospheric band dayglow, on the other hand, provides information about ozone density (Evans et al., 1988; Mlynczak et al., 2001), which in turn is related to atomic oxygen through photochemical equilibrium. Gravity waves in the MLT can be inferred from these measurements by observing patterns in either airglow volume emission, odd oxygen, or temperature. Among these, analysing gravity waves in the temperature field is most beneficial as temperature is directly connected to the basic state of the atmosphere and as gravity wave momentum flux becomes accessible (Ern et al., 2004). To this end, temperature amplitudes as well as horizontal and vertical wavelengths need to be inferred from the measurements.

NLCs are measured by MATS using two spectral channels in the ultraviolet at 270 and 305 nm. While imaging at one wavelength is sufficient for analysing global NLC variations and local NLC structures, the use of two wavelengths gives the additional benefit of accessing particle sizes and ice content. To this end, the observed spectral dependence of NLC signal is fitted in terms of an Ångström exponent and compared to numerical scattering simulations (von Savigny et al., 2005; Karlsson and Gumbel, 2005). For typical NLC particle sizes, observations in the ultraviolet are preferable as they push the scattering deeper into the Mie regime, thus maximizing the amount of information that can be inferred from spectral measurements. In addition, wavelengths below 310 nm are efficiently absorbed by the stratospheric ozone layer and are therefore chosen to avoid complications due to upwelling radiation. For MATS, the concrete wavelengths 270 and 305 nm are chosen both to ensure a sensitive retrieval in the NLC particle size range of interest (Sect. 4.6), and to minimize potential perturbations due to atmospheric emission features (airglow, aurora). The tomographic NLC data will be the basis for gravity wave analysis in terms of horizontal wavelengths. The vertical structure of the NLCs is strongly determined by the microphysics that governs cloud growth and sedimentation (Rapp and Thomas, 2006). The tomography will provide detailed insights into this vertical NLC evolution, including its possible modification by wave activity (Hultgren and Gumbel, 2014; Megner et al., 2016; Gao et al., 2018). However, since the vertical structure of the narrow NLC layers is dominated by microphysics rather than dynamical processes, a retrieval of vertical wavelengths of gravity waves will not be feasible from the NLC data.

The limb instrument will be described in Sect. 3, and details of the tomographic and spectral retrievals will be given in Sect. 4. Table 1 summarizes the above retrieval products from the MATS limb measurements. The table also states the required precision and spatial resolution of these retrieval products. These requirement are defined by the need to infer relevant gravity wave data from these retrieval products, in accordance with the overall objectives listed in the Sect. 2.1. Note that typical values are given for precision and resolution. These parameters depend on the altitude-dependent signal strengths. They are also adjustable as, for example, enhanced image binning can improve precision at the cost of resolution. These trade-offs will be further illustrated in the following sections.

In addition to these MATS limb measurements, an auxiliary nadir imager will take pictures of the O2 atmospheric band emission from below the satellite. This provides complementary information on smaller spatial scales down to 10–20 km horizontal resolution, albeit restricted to a detection of structures rather than a detailed spectroscopic analysis. During sunlit (or moonlit) conditions, nadir measurements of airglow layers get drowned in background light from the lower atmosphere. Gravity wave data from the MATS nadir camera will therefore be restricted to moonless nights. The near-terminator orbit of MATS is not optimal for such nightglow studies as sufficiently dark measurement conditions will only be available during the winter season at mid-latitudes and high latitudes. From the ground, nightglow imaging is a standard technique for local measurements of gravity waves in the MLT (e.g. Taylor et al., 1997; Espy et al., 2004). An obvious advantage of satellite measurements is global coverage; however, this comes with the disadvantage of lacking temporal coverage at a given location. Also, nadir imaging from a moving satellite is subject to image smearing (motion blur), thus implying a restriction to short integration times and strong wave features.

Original ideas for MATS date back longer than the current project development. A first mission concept was developed by Jacek Stegman and Donal Murtagh at Stockholm University in the 1990s, then under the name “Mesospheric Airglow Transient Signatures (MATS)”. An important heritage for MATS is also the Odin satellite mission, both concerning satellite, instrument, and operational concepts (Murtagh et al., 2002; Llewellyn et al., 2004). For the Optical Spectrograph and InfraRed Imager System (OSIRIS) on board Odin, tomographic ideas were developed by Degenstein et al. (2003, 2004). In 2010, special “tomographic” scan modes were developed for Odin, covering a limited tangent altitude range of about 75–90 km with relatively high horizontal repetition rate. These measurements provided input to tomographic and spectroscopic retrievals (Hultgren and Gumbel, 2014) that served as important tests for the MATS mission development.

The current MATS satellite mission was developed in response to a call by the Swedish National Space Agency concerning “Innovative low-cost research satellite missions”. MATS was selected after going through an initial mission definition phase in 2014.

An important basis for MATS is the InnoSat satellite platform developed by OHB Sweden and ÅAC Microtec (Larsson et al., 2016). InnoSat has been designed as a “universal” microsatellite platform that can host a variety of different payloads for aeronomy or astronomy research in low-Earth orbit. MATS is the first scientific mission to use InnoSat. As a consequence, much of the development of platform and payload have been carried out in parallel. MATS has been designed to use the “baseline configuration” of InnoSat. Table 2 lists important parameters that define this configuration. All parameters in Table 2 constitute boundary conditions for the design and performance of MATS, as will be illuminated further in Sects. 3 and 4.

Behind the development of the MATS instruments and scientific mission is an Instrument Consortium comprising Stockholm University, Calmers University of Technology in Göteborg, and the Royal Institute of Technology in Stockholm, in collaboration with Omnisys Instruments (Göteborg), Molflow (Göteborg), and Kyung Hee University (Republic of Korea). This is complemented by a Platform Consortium comprising OHB Sweden in Stockholm and ÅAC Microtec in Uppsala, the companies behind InnoSat. The MATS satellite is currently in preparation for a launch in 2020. The launch will take place in a piggyback configuration to an orbit at an altitude around 600 km. The nominal time of the Equator passage is around 06:00 and 18:00 local time (LT), thus providing a “near-terminator” orbit.

The MATS payload comprises four optical instruments: the six-channel limb imager and the nadir camera measure mesospheric emissions, as introduced in the previous section. A pair of nadir-viewing photometers measures upwelling radiation from the Earth surface and lower atmosphere, in support of the limb instrument analysis. A star-tracking camera directed in the opposite direction of the limb imager ensures accurate pointing of the satellite. Figure 2 shows the overall configuration.

The sun-synchronous polar orbit with nominal Equator passage near 06:00 and 18:30 LT is beneficial for an efficient satellite design. It ensures that the satellite receives sunlight largely during the entire mission, and that a solar panel mounted at one side of the platform is sufficient to make use of this sunlight. In addition, instruments and electronics will be shaded behind the solar panels during the mission. As for the field of view, the satellite will nominally be oriented so that the limb instrument looks backwards along the orbit. This provides the necessary overlap between subsequent images as input to the tomography retrieval.

Since the goal is to investigate both NLCs and O2 atmospheric band emission, two separate wavelength regions will be measured by MATS. As described in Sect. 2.2, two UV channels will be used for the NLC study. To measure the atmospheric band emission, two main channels are used: a wideband channel covering the entire 0–0 vibrational band, and a narrowband channel covering only the centre. In order to quantify the effect of background radiation and straylight on the atmospheric band measurements, a set of ancillary measurements are done using two background IR channels of the limb imager, as well as the pair of nadir-looking photometers that provide information about upwelling radiation both within and outside the atmospheric band. In order to achieve the MATS measurement objectives (Table 1), four basic tasks have been central to the limb instrument design: imaging quality, sensitivity (signal-to-noise ratio), spectral separation, and straylight suppression. Boundary conditions for the design are defined by the InnoSat satellite platform in terms of mass, dimensions, power etc. (Table 2). Figure 3 shows the overall layout of the limb imager.

Each of the two albedo photometers consists of a two-lens telescope based on standard N-BK7 lenses, providing a field of view of 6∘. In front of the telescope a pair of interference filters is placed on each photometer to discriminate against unwanted wavelengths. Baffles minimize straylight from outside the field of view. The detector is a Hamamatsu S1223-01 Si PIN photodiode. The system measures upcoming radiation at 759–767 and 752.5–755.5 nm, corresponding to the limb imager channels IR2-ABand-total and IR3-BG-short, respectively (Table 4). The signal-to-noise ratio is better than 100.

The nadir camera is a Cooke triplet with an entrance pupil of 15 mm, and an effective focal length of 50.6 mm. Its field of view is 24.4∘×6.1∘. From orbit, this covers an area of at least 200 km across track and 50 km along track at 100 km altitude. The design can resolve 10×10 km features at this altitude. Additional degradation occurs in the along-track direction due to smearing caused by the satellite movement during the exposure and readout phase. Figure 6 shows a sample image taken by a prototype nadir camera from the ground. In orbit, the nadir measurements aim at nighttime conditions, with the Sun located at least 10∘ below the horizon for a ground-based observer. However, under these conditions the satellite will be fully illuminated by the Sun, and straylight handling is thus essential for the nadir camera. Similar to the limb instrument, in addition to being mounted in the shadow of the solar panel, efficient straylight suppression for the nadir camera is achieved by a baffle with black coating on the inside.

The readout of the nadir camera uses the same readout electronics as the limb instrument (Sect. 3.2.4), albeit operated in a different readout scheme. The satellite moves at a speed of about 7 km s-1, and in order to limit motion blur, nightglow images are taken with an exposure time no longer than 1 s. Exposures are taken and the CCD is read out at a rate sufficient to obtain overlapping images along the ground-track of the satellite. The result is a continuous nightglow image swath of width 200 km along the night part of the orbit.

The data produced by the instruments on board MATS require several processing steps. The three major steps are as follows:

Level 0 – geolocating the images and adding meta-data relevant for further processing.

After geolocation and time-tagging, each image from the limb channels must be calibrated such that the image displays the radiance falling on each binned image pixel on the CCD. To do this, a parameterized model of the instrument has been developed that takes into account transmissivity of the optics, dark current and quantum efficiency variations with temperature, readout smearing, and readout bias and gain variations in the readout electronics. Each of these effects behaves differently and must be measured and modelled separately. The parameters used in this modelling are a combination of pre-flight calibration measurements, and in-flight corrections to these parameters via special calibration modes (Sect. 5.2).

Before the limb radiances can be analysed in terms of airglow or NLCs, two unwanted contributions to the signal must be removed: background light originating from within the nominal field of view, and straylight originating from outside the nominal field of view. Background from inside the field of view comprises both unwanted emissions (airglow, aurora) and scattered light (in particular molecular Rayleigh scattering). Straylight from outside the field of view can reach the CCDs by scattering in the baffle, scattering from imperfect or dusty surfaces of the optical elements (in particular the primary telescope mirror), and/or scattering from structures inside the instrument housing. Although the design of the limb instrument is optimized for out-of-field rejection, some straylight signal is to be expected. To remove this signal, both amplitude and non-uniformity across each CCD need to be estimated. As described in the following subsections, the amplitude will be estimated by combining information from several channels and tangent altitudes. The non-uniformity will be parameterized based on the straylight modelling and testing carried out prior to launch (Hammar et al., 2018).

The discrimination of unwanted and wanted radiances also needs to take account possible polarization effects. Based on pre-flight analysis, a potential source of polarization sensitivity of the MATS instrument are the beamsplitters mounted at 45∘ to the incoming beam. Polarization properties of the individual instrument channels are measured pre-flight, and can partly also be inferred in orbit, based on measurements against polarized atmospheric Rayleigh scattering under varying role angles of the satellite. Once the instrument's polarization properties are determined, their effect on the limb measurements can be taken into account in the retrieval. However, as different contributions to the total signal (airglow, NLC scattering, molecular scattering, straylight) can be expected to feature different degrees of polarization, some assumptions are needed to handle polarization in the retrieval: in the UV, single scattering will be assumed both for the light scattering of the clouds and the background Rayleigh scattering. This is motivated by the efficient absorption of upwelling UV radiation from the lower atmosphere by the stratospheric ozone layer. In the IR, while unpolarized radiation can be assumed from the airglow emission, the background radiation is more complex. Analysis carried out with the SASKTRAN radiative transfer simulator (Bourassa et al., 2008) indicates that the degree of background polarization will vary from between 0.1 and 0.2 depending on the albedo of the lower atmosphere, which can be estimated from the data obtained by the albedo photometers on MATS.

In general, contributions of background light and straylight to the total signal can be difficult to distinguish from each other. This is in part due to the fact that both wanted and unwanted signals are expected to vary in similar ways along the orbit. Most notable, upwelling radiation, and thus local conditions at lower altitudes, will affect O2 atmospheric band dayglow, NLC scattering, molecular Rayleigh background, as well as straylight. In the MATS data processing, the procedures for removing background and straylight are therefore closely linked.

As for the removal of background and straylight from the O2 atmospheric band channels, the two IR background channels (Table 4) provide the starting point. The amplitude of the straylight is estimated from the signals seen in the IR background channels at the highest altitudes, where we expect negligible contribution from other sources of light. The background from the nominal field of view, on the other hand, is estimated using the full background channel images. This compensates not only for the Rayleigh background, but also for the possible presence of NLCs, and for other airglow and possibly auroral emission features. The total contribution of these signals cannot be estimated by simple linear interpolation between the two IR background channels. Rather, these signals show distinct spectral dependence (Sheese et al., 2010). In particular, since O2 resonantly absorbs upwelling radiation in the atmospheric band itself, both scattered background and straylight are weaker than what would be expected from linear interpolation between the two background channels. To account for this, the lower atmospheric albedo needs to be quantified, regarding both absolute albedo and relative flux inside and outside the atmospheric band, which in turn depends on lower atmospheric cloudiness and cloud top height. This will be monitored by the pair of nadir-looking albedo photometers on board MATS that measure upwelling radiation inside and outside the atmospheric band. In combination with radiative transfer simulations of the relevant processes (Bourassa et al., 2008), this provides a more quantitative straylight and background correction, following the method described by Sheese et al. (2010).

As for the removal of background and straylight from the NLC channels, signals of concern are molecular Rayleigh background and straylight. Because of efficient absorption of UV radiation by stratospheric ozone, the major source for out-of-field straylight is Rayleigh scattering in the upper stratosphere, and the amount depends on the atmospheric ozone abundance and solar position. Similar to the IR, the amplitude of straylight will be estimated by assuming that the signal seen at the highest altitudes in the NLC images is completely dominated by straylight. As an option, Rayleigh background and the straylight will be removed only after the tomography has been completed. This is done to combine information from both spectral channels and from as many images as possible to estimate the Rayleigh scattering and straylight, which can be assumed to vary slowly in the horizontal direction. Atmospheric density profiles from an atmospheric model (NRLMSISE-00) will provide an initial estimate of the molecular Rayleigh background in the field of view. This estimate can then further be improved by normalizing it to the scattering observed under cloud-free conditions.

Tomography will be applied on the images to reconstruct three-dimensional fields of atmospheric emission (or scattering). This will be done using an iterative maximum a posteriori (MAP) method (Rodgers, 2000). Here the 3-D field of emission is described by a state vector, x, and the measured limb radiances by the measurement vector, y. These vectors are related via a linear forward model: 1y=Kx. K is the Jacobian matrix and describes how emissions x from locations throughout the measurement volume contribute to radiances y from individual limb lines of sight. K thus contains the physics of the measurement, including observation geometry, radiative transfer, and instrument characteristics. For the MATS retrieval processing, K will be geometrically calculated on a grid using a spherical (rotating) Earth geometry. Absorption by ozone (in the UV channels) and self-absorption (in the atmospheric band channels) will be included using a pre-existing climatology to calculate the optical depth along the path.

Assuming that we have some a priori knowledge about the atmospheric emission described by the vector x^ and a covariance matrix Sa, the maximum a posteriori state, x, can be found using Bayesian estimation by solving the equation 2x^=KTSe-1K+Sa-1-1KTSe-1y-Kx, where Se is the covariance matrix for the measurement vector y.

For large scale problems, inverting Eq. (2) can become extremely memory-intensive to the point where a direct solver based on decomposition is no longer a possibility. Thus, the equation needs to be solved iteratively. Ungermann et al. (2010) have shown that this can be done efficiently by rewriting the equation above as 3KTSe-1K+Sa-1x^=KTSe-1(y-Kx) and solving it iteratively using the conjugate gradient method.

As Fig. 1 illustrates, the MATS observation geometry provides a large number of lines of sight through a given atmospheric volume. However, a challenge for the MATS tomographic retrieval is that lines of sight only span over a limited range of observation angles (6∘), and that lines of sight cover very long paths (hundreds of kilometres) through an airglow layer or NLC layer. Tomographic retrievals under these conditions have been discussed by Krisch et al. (2018).

To illustrate the feasibility of the tomographic reconstruction, a prototype retrieval has been set up using a simple forward model with a pure spherical geometry (non-rotating Earth) and ignoring atmospheric absorption. A three-dimensional test field of NLC scattering coefficients is based on a combination of Odin/OSIRIS vertical profiles and AIM/CIPS images and covers a horizontal area of 5000 km along orbit and ±175 km across the track (Fig. 8a). Forward model simulations and retrievals are performed on a set of measurements covering roughly 3000 km along the track (containing 167 limb images to be processed), ±125 km on each side of the orbit plane, and altitudes from 60 to 100 km. The resolution of the grid is 20  × 6.4 km × 0.5 km in the along-track, across-track, and vertical direction, respectively. Measurements are simulated with random noise added assuming shot-noise-limited performance with signal-to-noise ratios defined by the instrument specification. The measurement covariance matrix is set correspondingly (diagonal elements only). The retrievals are performed with very lax constraints using an a priori atmosphere equal to the background atmosphere and an a priori covariance matrix with only diagonal entries equal to 10-8 m-1 sr-1.

The result from this retrieval test is shown in Fig. 8b. For the area fully covered by MATS measurements, i.e. 2000–3000 km along-track and ±125 km across-track, the retrieval successfully reproduces the atmospheric field. For the area fully covered by the tomography, the mean square error amounts to 1.5×10-10 m-1 sr-1, which corresponds to a relative error of 3 % for a typical cloud brightness of 5×10-9 m-1 sr-1. As expected, some degradation can be seen on the edges due to limited tomographic information, with no information at the outermost regions where no measurement data are available. Along the track these effects will be mitigated by performing the retrieval on subsequently overlapping volumes along the orbit.

Following the tomographic retrieval of volume emission rates, the O2 atmospheric band is analysed to reveal temperature and oxygen densities. Starting point for the temperature retrieval is the ratio, R, of the signals in the two atmospheric band channels. Figure 9 shows the (re-)distribution of the rotational transitions in the 0–0 vibrational band as a function of temperature. With a lifetime of 12 s, the rotational distribution of O2(b1Σ) is in thermodynamic equilibrium up to altitudes around 120 km, and thus representative for atmospheric temperature. The filter curves of the two MATS atmospheric band channels (“total” and “centre”) have been chosen so that the ratio R provides maximum sensitivity to temperature in the temperature range of interest.

Using Gaussian error estimation and assuming the error from each channel is roughly equal, the random error in the retrieved temperature is 4ΔT=2ΔϵϵdTdR, where ϵ and Δϵ are the retrieved volume emission and its RMS error, and dT/dR is the sensitivity of the temperature to the ratio between the signals in the two channels. In order to achieve a temperature precision of 2 K, a signal-to-noise ratio ϵ/Δϵ better than 500 is needed, with can typically be achieved between 90 and 100 km altitude during daytime. It should be noted that the RMS error depends not only on the instrument, but also the covariance matrices used in the retrieval. The tomographic retrieval will apply horizontal and vertical regularization to suppress noise in the retrieved field. Hence, based on the true performance of the MATS instrument, further trade-off studies will be made between noise and spatial resolution in terms of measurement integration times, pixel binning, and regularization.

As stated in Table 1, possibilities to spectroscopically retrieve temperature from the O2 atmospheric band nightglow are more limited. When providing temperature data with the maximum tomographic resolution of 60 km × 20 km × 1 km, the precision at nighttime will be 5–20 K. Again, the temperature precision can be improved by spatial or temporal averaging, at the cost of reduced spatial resolution of the tomographic output. However this trade-off is handled, possibilities to retrieve gravity wave data from the temperature field are rather limited during nighttime. Notwithstanding this limitation of the temperature analysis, nighttime gravity wave data can be obtained directly from the tomographically retrieved spatial distribution of nightglow volume emission rates.

The total volume emission rate of the atmospheric band provides direct information about the concentration of excited molecular oxygen O2(b1Σ). This is also the basis for retrieving concentrations of ozone and atomic oxygen, which are intimately linked to O2(b1Σ) via dayglow photochemical reactions (Evans et al., 1988). As compared to the more complex daytime retrievals, the atmospheric band nightglow emission is largely only dependent on atomic oxygen, which allows for rather direct retrieval of atomic oxygen concentrations (Sheese et al., 2011).

The tomographic retrievals from the MATS UV channels provide the amount of scattered sunlight by NLCs throughout the 3-D retrieval grid. Additional NLC information will be available from the atmospheric band background channels, thus providing complementary spectral NLC data in the infrared. The ratio of NLC-scattered sunlight to solar irradiance provides the volume scattering coefficient β in each retrieval pixel.

The amount of light scattered from ice particles depends largely on the ratio between the size of the particle and wavelength of the light. Rayleigh scattering applies to particles much smaller that the wavelength, with the scattering coefficient approximately proportional to λ-4. (Note that even in the Rayleigh limit the exponent is not exactly 4, as spectral dependence of the ice particles' index of refraction causes an additional wavelength dependence.) For larger particles, interactions with the incoming sunlight get more complicated, and the scattering can be described as Mie scattering for spherical particles, or more complex numerical schemes for non-spherical particles (e.g. Mishchenko and Travis, 1998). Even in these more general cases, the wavelength dependence of the scattering in a limited spectral range can conveniently be described by a dependence λ-α, where λ is the wavelength, and α a size-dependent exponent, the so-called Ångström exponent (e.g. von Savigny et al., 2005). This Ångström description is frequently used in particle size retrievals, relating spectral measurements of particle scattering to theoretical descriptions of scattering as a function of particle size. For the two UV channels of the MATS limb instrument, the Ångström exponent is obtained as 5α=log⁡λ2-log⁡λ1log⁡β1-log⁡β2. Once the Ångström exponent in each tomographic retrieval pixel is determined, this value can be compared to scattering simulations of different ice particle distributions. Figure 11 shows an example of a lookup table connecting particle sizes and Ångström exponent for the MATS UV wavelengths. It is important to note, however, that the information that can be retrieved about the NLC particle population is limited: the Ångström exponent provides a single piece of information and can thus determine one parameter describing the size distribution, e.g. a mode radius. This makes it necessary to make assumptions about additional parameters describing the particle population. Here we use the same assumptions that have been used in earlier retrieval studies, e.g. for the AIM/CIPS or Odin/OSIRIS instrument. This includes oblate spheroid ice particles with an axial ratio of 2, and a normal distribution of particle sizes with a distribution width that varies with the mode radius (Lumpe et al., 2013; Hultgren and Gumbel, 2014). As Fig. 10 shows, the resulting relationship between Ångström coefficient and particle sizes will generally be ambiguous for larger mode radii exceeding about 100 nm. A method to remove this ambiguity is to involve information from the infrared channels in the retrieval (Karlsson and Gumbel, 2005). Physically, NLC particle populations are expected to have mode radii below 100 nm. Once particle size information has been inferred in the form of a mode radius, absolute scattering coefficient and size information can be combined to also retrieve the local ice content (ice mass density) of the cloud.

Through Gaussian error propagation the error in the Ångström parameter in a retrieval pixel can be estimated through 6Δα=2log⁡λ1-log⁡λ2Δββ, where Δβ is the uncertainty of the retrieved volume scattering coefficient, assuming it is roughly equal for the two wavelengths. From this, the error in the mode radius and ice mass density can be estimated through scattering simulations. In order to achieve a precision of 0.25 in the Ångström exponent, a signal-to-noise ratio β/Δβ better than 50 is needed.

As described in the previous sections, tomographic and spectroscopic analysis will provide three-dimensional fields of airglow emission rate, temperature, oxygen species, and NLC properties. These primary data products have been summarized in Table 1. All of these data fields can serve as input to an analysis of gravity waves and other atmospheric structures. However, there is a particular interest in wave retrievals from the temperature field as it allows for the analysis in terms gravity wave momentum flux (GWMF), potential energy density, and other quantitative wave properties (Ern et al., 2004; Fritts et al., 2014). The gravity wave retrieval involves several steps. The starting point is to infer spatial temperature variations, after calculation of a mean background temperature field. The three-dimensional temperature variations are then the basis for identifying horizontal and vertical wavelengths or wave numbers. Subsequent analysis builds on basic wave relationships as described, for example, by Fritts and Alexander (2003). Applying the dispersion relation, intrinsic frequency and group velocity can be inferred from wave numbers and background temperature. This is the basis for a subsequent retrieval of directional GWMF (Ern et al., 2004, 2011). This also needs (climatological) data on atmospheric density. Retrieval at multiple altitudes allows for an analysis of vertical GWMF gradients, and thus the momentum forcing (wave drag) of the background flow. An important goal is to obtain seasonal and latitudinal climatologies of gravity wave spectra, and to identify the contribution of different wavelengths to GWMF and wave drag. Such an analysis requires knowledge about a sensitivity function, i.e. the response of the MATS wave retrieval in terms of a wave's horizontal and vertical wavelength, and orientation, as well as observation conditions. Detailed descriptions of wave retrievals and sensitivities are beyond the scope of the current paper and will be provided in future publications about MATS data products.

In order to demonstrate MATS' ability to reconstruct gravity wave structures, the tomographic method has been tested on a set of coherent gravity waves observable in the atmospheric band emission. The emission field is generated using a simple airglow gravity wave model (Li, 2017). Using the same forward model as for the NLC simulations (Sect. 4.4), MATS limb instrument images are simulated, and the three-dimensional emission fields are retrieved using the MAP method. A total of 200 images have been simulated, covering 6000 km along-track and 400 km across-track with a resolution of 5 km × 5 km × 0.25 km.

This has been tested for wave structures aligned both along the movement of the satellite and perpendicular to it. As part of these tests, the horizontal and vertical wavelengths are varied. The amplitude of the retrieved wave is then compared to the amplitude of the true wave field. The ratio between these indicates the contrast in the retrieved data and is referred to as the gravity wave sensitivity for a certain wavelength (Preusse et al., 2002). Figure 11a shows the sensitivity for along-track waves, i.e. waves with fronts aligned perpendicular to the satellite track. Gravity waves with horizontal wavelengths down to 60 km and vertical wavelengths down to 3 to 5 km can be detected with a contrast better than 0.8. Panel (b) shows the sensitivity for across-track waves, i.e. waves with fronts parallel to the satellite track. For this wave geometry, vertical wavelengths can be inferred down to 3 km with a strong signal, and horizontal wavelengths can be retrieved down to 20 km, only limited by the resolution of the limb image. For both along-track and across-track waves, wave structures with vertical wavelength down to 1 km can be detected, albeit with a reduction in amplitude by more than 50 %.

When defining operational measurement modes, an important constraint is the total data volume as defined by the satellite's downlink capacity. Hence, compromises must be made concerning image resolution, image compression, sampling interval, geographical coverage, and the number of channels in operation. “NLC modes” will be active during the NLC season, i.e. summer months in either hemisphere. During that period, the UV limb channels are given priority to operate at high resolution at summer latitudes poleward of 45∘. The resolution of the IR limb channels is kept moderate in order to keep data volumes down. “IR modes” will be active outside the NLC season and involve no data collection in the UV channels, which allows the IR channels to operate at higher resolution. The IR nadir camera will always be operated during nighttime, producing a rather small data volume. Tables 5 and 6 summarize basic instrument settings in NLC and IR modes. Note that the exact values listed in the tables are preliminary. They are subject to change depending on the in-orbit performance, as will be established during the commissioning phase. The resulting measurements are the basis for the retrieval of the primary data product listed in Table 1.

In addition to the instrument settings in Tables 5 and 6, the platform attitude can be adapted in accordance with specific measurement objectives. A standard viewing geometry is to take subsequent limb images centred around the satellite orbit plane. At the highest latitudes, this provides aligned images as input tomographic retrieval. However, at lower latitudes the Earth rotation leads to a continuous shifting of the atmospheric scene with respect to the orbit plane. MATS provides the option to compensate for this in terms of a continuous yaw movement of the satellite. This movement lets the limb field of view follow the Earth rotation, thus keeping a targeted section of the atmosphere aligned between subsequent limb images.

In addition to the above science modes, a number of measurements are to be performed to characterize the instrument in orbit. Calibration measurements will be carried out with certain intervals, and involve changes in control settings for both the payload and the platform. Moreover, special manoeuvres can be performed to verify the integrity of the instrument after launch or on other occasions.

The driver for these calibration and special modes is that instrument properties may change in time, and need to be monitored. Table 7 lists main properties in this regard, including satellite operations and timescales over which changes can occur. These properties may in turn be dependent on operational parameters like solar position, instrument temperature etc., and should be monitored together as a function of those, if applicable. For these characterization activities, dedicated attitude operations have been defined for the platform, e.g. providing the possibility to point towards the lower (Rayleigh scattering) atmosphere, dark space, the moon, or stars. During these measurements the CCDs may be operated with different integration times, with reduced pixel binning or full image readout.